(Abridged) We examine the radial entropy distribution and its scaling using 31 nearby galaxy clusters from the Representative XMM-Newton Cluster Structure Survey (REXCESS). The entropy profiles are robustly measured at least out to R_1000 in all systems and out to R_500 in 13 systems. Compared to theoretical expectations, the observed distributions show a radial and mass-dependent excess entropy that is greater and extends to larger radii in lower mass systems. At R_500, the mass dependence and entropy excess are both negligible within the uncertainties. Mirroring this behaviour, the scaling of gas entropy is shallower than self-similar in the inner regions, but steepens with radius, becoming consistent with self-similar at R_500. The dispersion in scaled entropy in the inner regions is linked to the presence of cool cores and dynamical activity; at larger radii the dispersion decreases by a factor of two and the dichotomy between subsamples disappears. Parameterising the profiles with a power law plus constant model, there are two peaks in central entropy K_0; however, we cannot distinguish between a bimodal or a left-skewed distribution. The outer slopes are correlated with system temperature; their distribution is unimodal with a median value of 0.98. Renormalising the dimensionless entropy profiles by the gas mass fraction profile f_gas(< R), leads to a remarkable reduction in the scatter, implying that gas mass fraction variations with radius and mass are the cause of the observed entropy properties. We discuss a tentative scenario to explain the behaviour of the entropy and gas mass fraction in the REXCESS sample, in which extra heating and merger mixing maintains an elevated central entropy level in the majority of the population, and a smaller fraction of systems develops a cool core.
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